Safari Auto-Sharing Bookmarks: How do I stop it?

I have a Mac desktop and a MacBook Air. The MacBook air is only used for certain projects: most every file I use is saved in the iCloud; anything of a sensitive nature is not kept here. That is the way I want it, but Safari had different ideas.

When I got the laptop, most - but not all - of my bookmarks from my desktop were automatically added to the laptop. This wasn't a transfer; I still use the laptop for most of my work. I'm guessing it was done because of my appleID, I don't really know, but in any event, I do not want this. There are only a few bookmarks I would like to have on the laptop, the rest should not have ever of been addedd. I don't know how this was set up, but I would like to stop it.

I am tempted to just delete them all from the laptop, but - as I have no idea how or why they were auto-populated - I am fearful that deleting bookmarks on the laptop will work backwards and delete them off the desktop.

I would appreciate any advice on how to stop they two from "sharing" bookmarks and know how to safely remove them from the laptop. If your suggestion is to question why I want to do this, please do not bother posting.

Thanks

Jim